Slender Columns Research Articles

Full‐Scale Beam‐To‐Column Subassemblage Testing for Seismic Evaluation of Deep Columns

ABSTRACTSteel moment frames composed of wide‐flange steel members are commonly used in seismic regions, with deep and slender column sections often selected to economically satisfy drift limit requirements. The section slenderness makes the columns more susceptible to local and global buckling and subsequent axial shortening when subjected to combined high axial forces and lateral deformations. Numerous tests have been conducted on individual column members under a wide range of axial loads and loading patterns. Experimental data of subassembly or complete frame configurations providing insight into system level interaction of the column with the frame are more limited. To address this concern, a full‐scale testing program was conducted on four cruciform beam‐to‐column subassemblage subjected to loading patterns based on cyclic quasi‐static and slow hybrid simulation. Quasi‐static tests followed standard AISC loading protocol with constant column axial load ranging from 20% to 40% of the yield capacity. Advanced hybrid simulations subjected the specimens to realistic earthquake loading patterns to levels consistent with design basis earthquake (DBE) and maximum considered earthquake (MCE) ground motions. A full nonlinear model of a complete 6‐story frame was developed for the numerical substructure in the hybrid simulation. The observed local and global responses of two quasi‐static and two hybrid tests are presented, providing valuable data towards improving the understanding of progress of damage for these systems through advanced testing techniques.

On the Buckling Behavior of DLP 3D Printed PLA with AgNO<sub>3</sub> Addition

The antibacterial effects of AgNO3 have been observed and utilized in various applications. However, only a few studies have examined its effects on the mechanical properties of a matrix when combined. In this study, AgNO3 was used as an additive and blended with PLA resin for 3D printing to study its impact on buckling behavior, which is critical for designing slender column structures. To prepare the mixture, several processes were undertaken: (1) dissolving AgNO3 in distilled water; (2) adding the dissolved AgNO3 into the PLA resin; (3) stirring; (4) degassing; and (5) re-stirring. Based on the experimental results, the addition of AgNO3 led to a decrease in the buckling strength of PLA. For pure PLA specimens, the critical buckling stresses are 47.92, 44.91, 29.72, and 17.11 MPa for lengths of 10, 50, 100, and 150 mm, respectively. For the PLA + 2% AgNO3 specimens, the values are 23.55, 18.89, 15.1, and 10.48 MPa for the same lengths. Moreover, when compared to the theory using the Johnson and Euler buckling formulas, the obtained experimental results show good agreement.

Parameter priority of stub and slender rectangular CFDST columns subjected to eccentric loading

AbstractThis paper evaluates the behavior and ultimate load that previously identified parameters have on stub and long slender rectangular concrete‐filled double skin tubular (CFDST) columns subjected to eccentric loading. The investigation was performed using FE models that were calibrated and validated to eccentrically loaded experimental responses. A parametric investigation was thereafter conducted on seven parameters to establish the parameter priority on stub and long slender rectangular CFDST columns subjected to eccentric loading. The strong and weak axis minimally affects the parameter priority for a particular slenderness ratio. The investigation revealed that the parameter priority is different for stub and long slender columns. For load eccentricity, lateral curvature, steel strength, outer tube thickness, concrete strength, fixity, and inner tube thickness affect the ultimate load by 60.2%, 14.0%, 8.1%, 8.0%, 4.3%, 3.4%, and 2.1%, respectively, when compared to all parameters. For long slender columns, the load eccentricity, fixity, outer tube thickness steel strength, lateral curvature, concrete strength, and inner tube thickness affect the ultimate load by 70.7%, 10.6%, 6.2% 5.9%, 2.4%, 2.3%, and 2.0%, respectively, when compared to all parameters.

Partially encased composite steel and concrete columns: a systematic approach to the literature

Partially encased composite columns emerge as a promising solution in structural engineering, combining the versatility of steel with the durability of concrete. This article explores their characteristics and advantages, highlighting the construction efficiency and resource savings they offer compared to traditional reinforced concrete structures. While steel provides strength and speed in construction, concrete offers protection against fire and compression. The study consisted of two stages: the systematic literature review, in which the most relevant bibliography for the objective of the article was selected, and the meta-analysis stage. The studies indicated a decrease in the initial stiffness, maximum load and ultimate strength of the columns, with an increase in eccentricity, as well as an increase in the peak axial load and final moment of resistance in high-strength concrete, especially in slender columns which present reduced peak axial load due to the increase in the slenderness index. Furthermore, partially encased columns demonstrated superior compressive strength to steel at high temperatures. Therefore, these columns represent a promising option, subject to additional considerations and specific studies.

Numerical analysis and design of axially-loaded concrete-filled stainless-clad bimetallic steel tubular slender columns

Concrete-filled stainless-clad bimetallic steel tubular (CFBST) structures with stainless-clad bimetallic steel outer tubes combine the cost-effectiveness and high corrosion resistance of stainless-clad steel with the excellent load-bearing capacity inherent in traditional concrete-filled steel tubular (CFST) structures, making them well-suited for applications in demanding marine environments. This paper presents a comprehensive numerical study on CFBST slender columns with circular hollow section (CHS) outer tubes under axial compression. Finite element (FE) models were established and validated by comparing the load-axial displacement curves, ultimate loads, and failure modes obtained from the FE models with the existing experimental results. By employing the validated FE models, an extensive parametric analysis comprising 1120 models was undertaken to investigate the influence of length-diameter ratios, clad ratios and wall thicknesses of stainless-clad bimetallic steel outer tubes, as well as concrete strengths on the flexural buckling behavior of CFBST slender columns. The applicability of existing design codes for conventional CFST systems, including the European Standard EN 1994–1-1, Australian Standard AS/NZS 5100, American National Standard ANSI/AISC 360-22, as well as two Chinese Codes GB 50936-2014 and GB/T 51446-2021 was evaluated. It has been observed that the method outlined in EN 1994–1-1 is recognized for its accuracy in calculating flexural buckling resistance. However, it tends to yield overconservative predictions within the relative slenderness range of 0.2 to 0.35, where buckling effects are already considered. Consequently, a modification to EN 1994–1-1 has been proposed to adjust the limiting non-dimensional slenderness for CFBST slender columns to 0.35, thereby enhancing the accuracy and consistency in design capacity predictions.

Multilinear regression model for predicting the ultimate load of slender circular CFDST columns subjected to concentric and eccentric loading

AbstractThis paper presents a novel approach to predict the ultimate load of slender circular concrete‐filled double skin tubular (CFDST) columns subjected to concentric and eccentric loading. The proposed approach was developed using a multilinear regression model through analyzing a database containing 165 CFDST column configurations. The data set was obtained by varying the magnitude of the parameters to determine its effect on the ultimate load using FE analysis. The variables considered in the model formulation are concrete strength, steel tube strengths, tube diameters, tube thicknesses, load eccentricity, column curvature, and column length. The accuracy and efficiency of the proposed models were validated with previous experimental investigations. The results demonstrate that the proposed models provide a practical, simple, and efficient approach to predict the ultimate load of slender circular CFDST columns subjected to concentric and eccentric loading. When compared to existing experimental work on slender circular CFDST columns subjected to concentric and eccentric loading, the proposed model over predicts the ultimate load by a maximum of 6%.

Manuscript title: Experimental investigations of concrete-filled double skin steel tube column-column grouted connection under axial compression

This paper presents a novel grouted connection joint for prefabricated CFDST columns. In order to ascertain the reliability of this grouted connection, axial compression tests were conducted on 24 CFDST columns with grouted connections and 3 CFDST columns without grouted connections. The test parameters were grout strength, casing tube length, and length-to-diameter ratio. The results showed that the stub columns failed due to local buckling and the slender columns failed due to global buckling with significant lateral flexural deformation. CFDST columns with grouted connections exhibited a similar or even higher ultimate bearing capacity and much higher later bearing capacity than conventional CFDST columns. The ultimate bearing capacity of CFDST columns with grouted connections is influenced by the casing tube length and the length-to-diameter ratio. The increase in casing tube length leads to an increase in bearing capacity, while an increase in length-to-diameter ratio results in a decrease. Enhancing the grout strength does not significantly improve the ultimate bearing capacity. Furthermore, the effects of each test parameter on the stiffness, strength and ductility of the CFDST column-column grouted connections were evaluated. Finally, by considering the interaction between components and the impact of casing tube length on bearing capacity, a prediction equation for the ultimate bearing capacity of CFDST column-column grouting connections was developed. This equation can offer accurate predictions with an average error of less than 1 % to provide a reference for the joint design.

Experimental Investigation of Low-Cost Bamboo Composite (LCBC) Slender Structural Columns in Compression

This paper experimentally investigates the behavior of innovative sustainable Low-Cost Bamboo Composite (LCBC) structural columns under compressive loading. The LCBC columns are manufactured from bamboo culms in combination with bio-based resins to form composite structural columns. Different LCBC cross-sectional configurations are investigated in this study, including the Russian doll (RD), Big Russian doll (BRD), Hawser (HAW), and Scrimber (SCR). Two bio-based resins, including one bio-epoxies and one furan-based resin, in addition to a soft bio-based filler and a synthetic epoxy resin, are applied. The bamboo species used as the cast-in-place giant bamboo for all configurations include Moso, Guadua, and Tali. Slender LCBC columns showed maximum stress equal to 60 MPa at failure. The study found that the samples with bio-epoxy resin (BE2) exhibited enhanced material stiffness when compared to synthetic epoxy (EPX) and furan-based resin (PF1), while PF1 specimens demonstrated increased ductility. Among the specimens with Moso bamboo and BE2 resin, those with SCR and HAW configurations achieved the highest compressive strengths.

Stability of slender GFRP tube-confined UHPC-filled steel-encased column under axial compression: Experiment and mesoscale modeling

The stability of GFRP tube-confined UHPC-filled steel-encased columns (FUSCs) is critical for optimal utilization of its superior cross-sectional load-bearing capacity that guarantees overall structural safety. This study conducted an experimental investigation on 14 slender FUSC specimens under uniaxial compression for different aspect ratios and aggregate contents. The pressure-sensing films were applied to measure the contact pressure between the GFRP tube and UHPC, and a mesoscale finite element model was developed to uncover the role of randomly distributed fibers and aggregates in the UHPC during the failure process. Accordingly, the stability performance of slender FUSC was analyzed, and specific discussions were held on the mutual interaction mechanism between GFRP and UHPC during the loading process. The results showed that the stability of FUSCs decreased faster with an aspect ratio of l0/D > 8 (λ>30.77), resulting in the decrease of load-carrying capacity for up to 25 %. By including coarse aggregate, the distribution of steel fibers was densified, and Young's Modulus of UHPC was increased, considerably improving the stability of FUSCs. Moreover, the GFRP tube with a fixed winding angle of 50° remarkably enhanced the stability of the specimen due to the sharing of bending moment instead of providing confinement. This research outcome offers a basis for the stability control of slender FUSCs.

Impact of Eccentric Loading on the Structural Performance of Reinforced Concrete Pad Footings: An Experimental Study

Setting out of building footings are usually carried out using profile board. This method is usually not accurate in locating the position of columns. Hence, columns that are designed as a concentric columns to their respective footings ends up being columns having eccentricities to the pad footings that supports them. Since the stress distribution under pad footing with concentric column is different from that of pad footing with eccentric column, there is need to study the effect of these eccentricity on the load carrying capacity of the pad footing. In carrying out this work, four pad footings and a typical foundation were used. The pad footings were of sizes 230 mm x 230 mm x 150 mm, with columns of 150 mm x 150 mm cross-section. The first pad footing P1SH was pad footing with short column and zero eccentricity, the second pad footing P2SL was pad footing with slender column and zero eccentricity, the third pad footing P3SL was footing with slender column with 40 mm eccentricity, while the forth pad footing P4SL was footing with slender column with 80 mm eccentricity. The foundation comprises of sand which was contained in a sandbox. The sandbox was made of steel plate of dimensions 0.3 m × 0.3 m × 0.2 m of 4 mm thickness, was used to provide support for the foundation. The foundation was produced by compacting loose sand in three layers with 20 blows per layer in the steel box and with density of about 735 kg/m3. The pad footings were placed on top of the foundation contained in the sandbox, and together were placed on the loading plate of Universal Testing Machine (UTM). Compressive load was applied on each of the pad footings through the columns till failure occurred, using UTM. It was found out that pad footing P1SH have the highest load capacity of 261.25 kN, P2SL pad footing with load capacity of 124.24 kN, P3SL pad footing with load capacity of 39.34 kN, while P4SL pad footing with load capacity of 23.30 kN.

Eccentric compression behavior of CFRP-confined reactive powder concrete-filled steel tube slender columns

Ultra high and large-span structural components are needed in urban modernization construction to meet the engineering requirements. Reactive powder concrete-filled steel tubes (RPCFSTs) provide a cost-effective and efficient solution for optimizing space utilization in super high-rise buildings and enhancing the crossing capacity of bridge, which accords with such development. However, these components have inherent drawbacks in terms of local buckling and corrosion resistance. The use of carbon fiber reinforced polymer (CFRP) confinement to suppress this innate deficiency has been proven to show great advantages in limited trial results. This article establishes a comprehensive test scheme to investigate the eccentric compression performance of CFRP-confined RPCFST columns. A total of 11 specimens were prepared and subjected to biased compression test by varying the component length (400, 800, 1200, and 1600 mm), number of CFRP layers (0–3), and load eccentricity (0, 10, 20, 30, and 40 mm). The results showed that the CFRP confinement could effectively enhance the bearing capacity and energy dissipation capability of RPCFST columns while delaying the local buckling of slender specimens with low slenderness ratios. The improvement of ultimate load due to CFRP confinement exceeded 42.5 %. However, in specimens with higher slenderness ratios and with increasing load eccentricity, the confinement effect of the steel tube on the core RPC tended to weaken. An N–M interaction model for slender CFRP-confined RPCFST columns was established, and this model was validated to be in good agreement with the experimental results. The conclusions drawn from this study might given a solid foundation for the future application of CFRP-confined RPCFST structures.

Eccentric compression performance of jointed precast concrete-encased concrete-filled steel tube columns with dry connections

Concrete-encased concrete-filled steel tube (CECFST) columns have recently been regarded as the optimum option for high-rise or heavy-loaded buildings due to superior structural resistance over traditional concrete-filled steel tube (CFST) and reinforced concrete (RC). Thus, in developed countries with severe manpower shortages such as Singapore, advanced precast dry connections were proposed for the CECFST columns to facilitate construction and tackle manpower crunch. Moreover, current research shows that the proposed connection has comparable structural resistance with conventional cast-in-place (CIP) connections, demonstrating huge application potential. However, the existing research is only limited to the performance of precast connections without any experimental studies on jointed columns, which hinders the implementation of the precast connections in engineering of practices. In this paper, to address this research gap, a comprehensive experimental programme was initiated, followed by extensive numerical studies. A total of six intermediate and slender jointed precast columns were tested to investigate the effect of precast connections on load-carrying behaviour of the jointed CECFST columns by considering column slenderness, connection detailing, connection position and load eccentricity. Besides experimental studies, extensive 3D finite element (FE) simulations were performed to investigate the relationship between connection integrity, constructability, and load-carrying performance of the jointed CECFST columns. The numerical studies showed that implementing the conventional "Equivalent to CIP" concept into the design of jointed precast CECFST columns would significantly compromise the constructability of such columns. To address this concern, a performance-based design method was proposed for jointed CECFST columns. Parametric studies showed that adopting the performance-based design method could not only improve constructability but also achieve sufficient column resistance.

Design method for axially compressed H-sectional aluminium alloy slender column based on CSM

In this study, a section-limiting stress that considers the influence of cross-section slenderness on the load-carrying capacity proposed by the continuous strength method (CSM) is introduced for the first time in the design of axially compressed H-section aluminium alloy slender columns. Experimental and numerical simulation tests are conducted on these columns to understand their axial compression performance and failure modes, with subsequent validation of the numerical simulation methods. Using the CSM limiting stress, imperfection factor, and stability calculation factor, this study proposes a design method for the overall stability load-carrying capacity of axially compressed H-section aluminium alloy slender columns. The load-carrying capacity predictions of the proposed design method are compared with those of the European, American, Australian/New Zealand, and Chinese design standards using axial compression tests and numerical simulations. An evaluation of these design methods and standards is also presented. In addition, reliability analyses are conducted following the approaches proposed by the American Institute of Steel Construction and the European design standard to assess the reliability levels of the aforementioned design methods and standards. Finally, the study presents a calculation example of an aluminium alloy slender column using the proposed design method.

Shear strengthening and damage control effects of CFRP and self-prestressing iron-based SMA for concrete columns

Although prestressed shape memory alloy (SMA) has shown a great performance in flexural retrofitting of slender RC columns, its shear strengthening effect for squat RC columns has been barely studied. This study explores the shear strengthening and damage control effects of iron-based SMA (Fe SMA) for squat RC columns. The heat-activated prestressing of Fe SMA was evaluated first at material level, then applied to component level structural testing of RC columns. The four circular RC columns with different retrofitting schemes were tested under quasi-static lateral cyclic loading. The specimens strengthened with carbon fiber-reinforced polymer (CFRP) sheet and Fe SMA strip exhibited satisfactory global responses without showing significant shear failure. From the visual inspection and non-destructive damage assessment, the prestressed Fe SMA was found to be superior in delaying damage accumulation in concrete compared to CFRP.

Flexural behavior of precast concrete-filled steel tubes connected with high-performance concrete joints

Abstract Precast concrete-filled steel tube (CFST) columns with connection joints are widely used in building structures, yet research on their flexural behavior when connected with various high-performance concrete (HPC) types is limited. This study presents experimental investigations on precast circular CFST columns subjected to flexural loading until failure. These CFST columns, encased in galvanized steel sheets (GSSs), are connected using HPC joints. Two types of HPC joints were tested: an engineered cementitious composite (ECC) and an ultra-high fiber reinforced concrete (UHFRC). Additionally, the study was conducted varying the development length of the reinforcement/concrete filler joint to 150, 200, and 300 mm. Results indicated that increasing the development length of the reinforcement and the connecting concrete joint enhances both the cracking resistance and load-bearing capacity of slender precast CFST columns with an intermediate joint. Moreover, the combination of GSSs with ECC and UHFRC connections enhances the load-bearing capacity, demonstrating performance comparable to that of a typical precast normal concrete control column without an intermediate connection. The experimental results revealed that ECC and UHFRC connections increased the performance by 11 and 17%, respectively, compared to the control column. Additionally, doubling the development length of the ECC joint improved the cracking force, ultimate force, elastic stiffness, and energy absorption by 20, 15, 133, and 64%, respectively, while UHFRC connections showed improvements of 10, 10, 82, and 94%, respectively.

Experimental study on concrete-filled L-shaped steel tubular columns and beam-columns

Concrete-filled L-shaped steel tube (CFLST) is an efficient structural form for corner columns in high-rise buildings, which avoids column protrusion. This paper presents an experimental and theoretical study on the structural behavior of CFLST columns and beam-columns. A total of nine full-scale specimens (i.e., three stub columns, two slender columns, and four slender beam-columns) was tested under compressive loads and the specimen ends were free to rotate about a geometric axis. Plastic local buckling was observed for the stub columns and the confinement effect was not obvious. Flexural buckling occurred for the slender columns and beam-columns. With the increase in the applied load, the neutral axis shifted to the compressive side of the beam-column. Performance of current design codes, which apply for rectangular CFSTs, on predicting the ultimate capacities of CFLSTs was assessed. The prediction for section capacity was conservative and it was likely caused by the reduction in the design strength of concrete. The buckling curve in design codes for rectangular CFSTs was applicable for CFLST columns whereas the interaction relationship specified in design codes underestimates the ultimate capacities of CFLST beam-columns. Based on fiber element analysis, out-of-plane bending moment was found in the tested CFLST slender members and the values were quantified. A new interaction relationship was proposed for CFLST beam-columns, which exhibited good agreement with experimental and numerical results. Finally, design methods were recommended for CFLST columns and beam-columns.

Axial compression behaviors of square steel tubes at low temperatures

This paper investigated the compression behaviors of square steel tube (SST) columns used in cold-region engineering structures. Twenty-eight SST columns were tested at low temperatures of 20, −30, −60, and − 80 °C. The studied parameters were low temperature (T) and slenderness ratio (λ) of SSTs. Under low-temperature compression, stub columns (λ = 5) failed in local buckling whilst slender columns (λ = 15 and 25) failed in global buckling. Low temperatures exhibited marginal effects on failure modes, and slightly improved (less than 12 %) the ultimate compressive resistance (Pu) of SSTs. Decreasing T and λ values increased the compressive resistance of SSTs. Finite element (FE) models were established to simulate compression behaviors of SSTs at low temperatures, with accuracy confirmed by 28 test results. The FE parametric studies indicated that decreasing the width-to-thickness ratio of SSTs generally improved their compression capacity and ductility. Moreover, different code prediction formulae in GB50017, AISC 360–16, and Eurocode 3 for SSTs were checked to predict the Pu. Finally, prediction equations were developed to predict the compression resistance of SSTs at low temperatures. The prediction equations provided reasonable estimations on Pu with an average discrepancy of 4 %.

The ultimate capacity of geopolymer recycled aggregate concrete filled steel tubular columns: Numerical and theoretical study

Concrete-filled steel tubular (CFST) columns have been extensively used due to their numerous advantages including high load-bearing capacity, stiffness, energy absorption, and ductile failure mode. Human awareness toward environmental problems is increasing and research on geopolymer recycled aggregate concrete (GRAC) has gained much attention as a green and sustainable material. However, there is little experimental and numerical research on the behavior of CFST columns with the GRAC as an infill material with the available design codes not yet modified for addressing the utilization of unconventional concrete mixes, such as the GRAC. This research introduces a critical modification of the ACI code provisions using the nonlinear finite element analysis method (FEA) on the behavior of square GRACFST columns under axial compression where the proposed modification was verified using experimental data from the literature. The influence of the length-to-width ratio, width-to-thickness ratio, geopolymer concrete strength, and the recycled aggregate replacement ratio was investigated. Results show that the outward local buckling was the primary failure mode for both short and slender columns. Considerable improvements were observed in the column's load-bearing capacity, initial stiffness, ductility, and energy absorption by (81.0, 101.9, 46.5, and 87.8)%, respectively, achieved upon increasing the steel tube thickness from 3 mm to 9 mm. However, the increase in length-to-width ratio negatively affects the energy absorption by 39 % while the ductility was reduced up to 20.4 %. The predictability of the AISC360-16, ACI318-19, and BS5400-5 codes on the capacity of GRACFST columns was evaluated where conservative predictions were guaranteed with the closest one recorded for the ACI318-19 code with a 24.5 % overestimation percentage. Finally, a modification was proposed to the ACI code prediction, taking into account the inclusion of recycled aggregate and geopolymer concrete with only a 2 % average error.

An improved CSM-based design method for H-section aluminium slender columns under eccentric compression

This study proposed an improved design method for predicting the load-carrying capacity of H-section aluminium alloy slender columns under eccentric compression based on CSM. Through eccentric compression tests and extensive numerical simulations, the study explored the influence of cross-sectional dimensions, member slenderness ratios, and initial geometric imperfections on the load-carrying capacity of columns. The proposed CSM-based design method utilized CSM limiting stress and CSM buckling reduction factors tailored to aluminium alloy columns, accounting for the specifics of their material behavior and geometric properties. The comparison and evaluation of the load-carrying capacities predicted from the proposed design method, European design code, and American design code, as well as with experimental and numerical results, were conducted. Meanwhile, the reliability analyses on these design method and codes were also performed, adopting the method provided by the AISC and EN 1990, Annex D. The comparison and reliability analyses results indicate that, compared to existing design codes, the proposed CSM-based design method could provide more accurate, consistent, and reliable load-carrying capacities of H-section aluminium alloy slender columns under eccentric compression.

Axial compressive performance of CFRP-steel composite tube confined seawater sea-sand concrete intermediate slender columns

To alleviate the scarcity of river sand resources and fully utilize the advantages of Carbon Fiber Reinforced Polymer (CFRP), a new type of CFRP-steel composite tube was developed to confine seawater-sea sand concrete (FCTSSC) column structures. This study conducted experimental research on FCTSSC intermediate slender columns for the first time, analyzing their failure modes and working mechanisms. The investigation explored the effects of outer CFRP layers and slenderness ratios on the mechanical performance. The results indicate that the FCTSSC intermediate slender column specimens exhibited global buckling accompanied by local bulging of steel tubes as their failure mode. The load-displacement curves can be divided into strong confinement and weak confinement models. Specimens confined by CFRP exhibited a 12.51–31 % increase in ultimate bearing capacity. The ultimate bearing capacity and its enhancement rate were positively correlated with the outer CFRP layers and negatively correlated with the slenderness ratio. Peak lateral displacements were positively correlated with both parameters. Finally, the model for calculating the axial compression ultimate bearing capacity of FCTSSC intermediate slender columns was proposed, providing a reference for future practical applications in offshore engineering.